1. Field of the Invention
The present invention relates to devices and methods for determining a correlation value, which are useable, in particular, for digital transmission systems.
2. Description of Prior Art
For a receiver in a digital transmission system to be able to synchronize to a digital signal sent out by a transmitter, the transmitter radiates a digital signal known to the receiver. The receiver's task is to determine the precise time of arrival (TOA) of the signal sent. To determine the time of arrival, the cross-correlation between the digital receive signal and the known digital transmit signal is calculated. Subsequently, the magnitude maximum of the cross-correlation is detected, and the time of arrival of the transmit signal is determined from the position of the correlation magnitude maximum.
The existence of a carrier-frequency offset between a transmitter and a receiver may lead to a “self-extinction” of the cross-correlation from a certain length of the transmit signal, i.e. the individual addends in the cross-correlation add up to zero due to a complex rotation term caused by the carrier-frequency offset.
In the following example, a perfect transmission with the exception of a carrier-frequency offset between a transmitter and a receiver and with a constant channel coefficient a and a delay L shall be assumed. If a T burst x[k], to be transmitted, of a length t_burstlen, abbreviated by the variable K in the following, is stored in the transmitter, the receiver receives the complex baseband signaly[k+L]=α·x[k]·ej(2πΔFk+φ0),wherein ΔF=maxfreqoffsppm·10−6·carfreq/B_clock is the frequency offset normalized to a B_sample clock. That is, per B_sample, the phase difference between x[k] and y[k] increases by 2 nΔF radiant. This receive signal y[k] now is to be correlated with the original signal x[k] stored in the transmitter and receiver.
With maxfreqoffsppm=30, carfreq=2.445 GHz and B_clock=101.875 MHz, for example the phase per B_sample changes by 0.0045 radiant, or 0.00072, respectively, from the full circle. Thus, the phase difference cycles the full circle once between x[k] and y[k] within 1,389 samples.
The cross-correlation between the receive signal y[k] and the correlation sequence x[k] is now defined as
            r      yx        ⁡          [      l      ]        =            ∑              k        =        0                    K        -        1              ⁢                  y        ⁡                  [                      k            +            l                    ]                    ·                                    x            *                    ⁡                      [            k            ]                          .            
The index 1 here indicates by how much y[k] is to be shifted in the correlation calculation. In the receiver, we are interested in the t_nocorrvals correlation values for indices 1=0, . . . , t_nocorrvals−1.
When y[k] thus shifted is shifted by L B_samples, so that y[k+L] and x[k] match in an optimum manner, we obtain
            r      yx        ⁡          [      L      ]        =            ∑              k        =        0                    K        -        1              ⁢                  α        ·                                                        x              ⁡                              [                k                ]                                                          2                    ⁢              ⅇ                  j          ⁡                      (                                          2                ⁢                                                                  ⁢                πΔ                ⁢                                                                  ⁢                Fk                            +                              ϕ                0                                      )                              as a correlation value.
Let us assume that |x[k]|2 is constantly=C and that the entire T burst has a length of exactly K=1,389 B_samples, then the above correlation calculation corresponds to a summation over a complex-valued pointer of a constant length which rotates by exactly one full circle in the course of the 1,389 B_samples. The rotation of the pointer is shown in FIG. 16, the figure representing the plane of complex numbers.
It may be seen that the summation for the correlation value in this example results in ryx[L]=0 even though x[k] and y[k+L] are an optimum match. With this carrier-frequency offset and this T-burst length, the determination of the length of the T burst x[k] within the receive signal y[k] with the help of the correlation sequence x[k] fails. As a result of an extinction of the correlation value due to a carrier-frequency offset, it is not possible, for example, to determine the correlation magnitude maximum. As a consequence thereof, a synchronization between the transmitter and the receiver of a transmission system is made more difficult, or data transmission may be flawed.